With my elementary students, in each class I choose the table who cleans up the best (not the quickest!). My older students (2-5) have their names put into a box as art stars; every Monday at morning announcements, my principal draws three names from the box and those students get to choose a prize from my "treasure box." For younger students, I give stickers to the art stars.

Yeah, those little ones can try your soul some days, haha. I think of
those days as times when it feels like I am trying to lasso jello!

Ok, here's my arsenal of tricks that I use when I get that old jello
feeling and feel like I'm totally worthless as a teacher at their
cleanup time:
1. "Everyone pick up 20 things to put away." For some reason this
ALWAYS works. They love counting??? I don't always do this. I save it
for times when NOTHING is happening in the way of cleanup and the are
all just having a ball being little imps!
2. On days when we use oil pastels, tell them they cannot wash their
hands until all of the oil pastels are put away and their pictures are
stacked neatly in the pile. Then, while they are washing their hands,
spray their tables with fantastic. As they dry their hands, tell them
to take some extra paper towels to go dry their tables. No need for
water. The fantastic and dry paper towels gets the pastels off the
table just fine without a sponge and water.
3. Make sure you DEMONSTRATE how to wring all of the water out of a
sponge before they go wipe their tables with sponges or you will have
lakes on your tables. Make a rule "no soap on the tables without my
permission" or you will have lather city. Keep towels in your room for
days when they get too much water on the table and don't sweat the small
stuff.
4. Make table folders for each table to put their work in. This
simplifies cleanup and handing out work at the start and end of a
period.
5. If you are having real trouble with a class disintegrating during
cleanup, I would talk to them about it at the very beginning of the
period and tell them how you feel. Then when it is time to clean up
again at the end, a few reminders should be all you need to see better
results. I've never used the table captain idea. I just hand pick some
kids to wash brushes, and when I see someone not doing anything helpful,
I tell them to pick up all the erasers, or pencils, or sharpies, or
scissors. Kids seem to like having a specific job to do. In fact, it's
hilarious sometimes to see someone get sort of bent out of shape because
I asked a second person to help them pick up pencils or whatever. As if
the job is so important that they want to do it all by themself.
There's a lot of weird psychology going on at cleanup time, isn't there?